Review report on master thesis of Khaled Alkhaled
“Game Theoretic Approach to Transportation Problem on Networks”

In the presented master thesis a transportation problem with many participants on a given network is considered.
Participants (players) try to reach a given node on network in a minimal time or with minimal costs. Different game theoretical models
are proposed and investigated. In one case the minimization of time by each of players is made under condition that the corresponding paths
of players do not intersect (do not contain common arcs or do not contain common vertexes). The case when the paths do not contain
common arcs was considered earlier but in the dissertation numerical experiments are presented also for this case. A reach family of Nash
equilibrium is constructed and in some sense the best Nash equilibrium defined.  The cooperative solution is also proposed and it happens
(which is natural in this case) that it also constitutes a Nash equilibrium. I  variety of numerical experiments is made comparing
cooperative, best Nash and min max time outcomes. The new and interesting model in the case when players form coalitions is also considered. It is
supposed that player inside one coalitions may use intersecting paths (paths with common nodes or common arcs) but bunches of paths of
different coalition must not contain common arcs or common nodes. Each coalition when acting as one player tries to minimize the total
transportation costs. The two level cooperative solution of the problem is proposed: on the first level the solution of the
cooperative game between players as coalitions and on the second level the cooperative solution on the level of coalitions to allocate the
costs of coalition between its members. Since the considered model can be viewed as dynamic game a time-consistency problem arises and this
problem is also successfully solved. A reach variety of numerical experiments are made and the results of experiments presented.

I evaluate the thesis as “excellent”.

Scientific supervisor, professor, Petrosyan L.A.

22.05.2022.